1.

Let `f(x)=[|x|-|x-1|]^(2)` Which of the following equation is/are correct? 1. `f(-2)=f(5)` 2. `f'(-2)+f'(0.5)+f'(3)=4` Select the correct answer using the code given below:A. 1 onlyB. 2 onlyC. Both 1 and 2D. Neither 1 nor 2

Answer» Correct Answer - A
Given `f(x)=(|x|-|x+1|)^(2)`
`f(x)={{:(1" "x le 0),((2x-1)^(2)" "0 lt x lt 1),(1" "x ge 1):}`
For x = -2
f(x) = 1 so f(-2) = 1
For x = 5
f(x) = 1 `rArr` f(5) = 1
Hence f(-2) = f(5)
Now, for x = -1
f'(x) = 0
f'(-2) = 0
For x = 0.5
`f'(x) = 8 rArr f'(0.5) = 8`
For x = 3
`f'(x) = 0 rArr f'(3) = 0`
`rArr f'(-2) + f'(0.5) + f'(3) = 8 ne 4`


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